Comparison of Smallest Eigenvalues for Fractional-Order Nonlocal Boundary Value Problems

Johnny Henderson
2019 Advances in dynamical systems and applications (ADSA)  
For 1 < α ≤ 2 a real number, we apply the theory of u 0 -positive operators to establish the existence of smallest positive eigenvalues and their comparison for the αth-order Riemann-Liouville linear differential equations, D α 0+ y(t)+λp(t)y(t) = 0 and D α 0+ y(t) + σq(t)y(t) = 0, 0 < t < 1, with each satisfying the nonlocal boundary conditions, y(0) = p i=1 a i y(ξ i ), 0 < ξ 1 < · · · < ξ p < 1, and y(1) = r j=1 b j y(η j ), 0 < η 1 < · · · < η r < 1.
doi:10.37622/adsa/14.2.2019.189-199 fatcat:ckfm5as5dnhq7kqq5lnf6sk62a